On homomorphic encryption using abelian groups: Classical security analysis

arXiv (Cornell University)

Abstract

In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their primitive requires choosing three groups $G$, $H$, and $K$. In their paper, Leonardi and Ruiz-Lopez claim that, when $G$, $H$, and $K$ are abelian, then their public key cryptosystem is not quantum secure. In this paper, we study security for finite abelian groups $G$, $H$, and $K$ in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.

Authors 6

1. Eleni Agathocleous

   Helmholtz Center for Information Security

   Affiliation as printed

   CISPA Helmholtz Center for Information Security ,

2. Vishnupriya Anupindi

   Austrian Academy of Sciences

   Affiliation as printed

   RICAM Austrian Academy of Sciences ,

3. Annette Bachmayr Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University ,

4. Chloe Martindale

   University of Bristol

   Affiliation as printed

   University of Bristol ,

5. Rahinatou Yuh Njah Nchiwo
6. Mima Stanojkovski

   University of Trento

   Affiliation as printed

   Università di Trento